Collineations of Subiaco and Cherowitzo hyperovals (Q1914924)

Let \(PG(2,q)\) be Desarguesian projective plane. The authors show that if \(q = 2^h\), where \(q > 64\) and \(h \not\equiv 2 \pmod 4\), then the subgroup of \(P \Gamma L(3,q)\) of order \(2h\) fixing Subiaco oval is cyclic and is the full collineation stabilizer of the Subiaco hyperoval. In addition, they consider Cherowitzo hyperovals in \(PG(2,2^h)\) \((h\) odd, \(5\leq h \leq 15)\). They show that a collineation fixing this set of points and one of the points (0, 1, 0) or (0, 0, 1) must be an automorphic collineation.